Cholesky decomposition of a square symmetric positive definite matrix A
is a lower triangle matrix L with positive diagonal elements such that
A = L L*.
LU decomposition of a square non-singular matrix A
is a tripple L, U, P of matrices of the same size such that
PA = LU, where P is a permutation matrix, L is a lower-triangle matrix
and U is an upper triangle matrix.
This program does the same as the built-in MATLAB function lu.